Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity

Abstract

We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters S and U can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands the flatness of the scalar manifold. The relationship between the finiteness of the electroweak oblique corrections and perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, then the one-loop finiteness of the oblique correction parameters S and U is automatically guaranteed. *

Matching and running sensitivity in non-renormalizable inflationary models

“…This approach has led Vilkovinsky and de Witt in the Eighties to build the covariant effective action [38,41], and it is ubiquitous to formulate multi-field dynamics in a covariant form [39,[42][43][44]. Recently there has been a renewed interest in using geometric covariant formalisms for instance in the context of SMEFT (and extensions) [45][46][47][48][49], to compute UV divergences of general relativity as an EFT [50] and to address the issue of frame equivalence (at quantum level) in scalar-tensor theories [51][52][53].…”

Perturbative unitarity in quasi-single field inflation

“…Perturbative unitarity constraints on general scalar field theories were nicely discussed in ref. [24]. A conclusion there is that in spacetime four dimensions, the model is UV complete at the tree-level only when the field space is flat.…”

“…Another typical example is derivative interactions in the scalar sector, i.e., the Higgs boson and the Nambu-Goldstone bosons that are eaten by the gauge bosons. If we focus on two-derivative interactions, perturbative unitarity requires flatness of the field space in the UV complete theory, which in turn specifies the scale of new physics to be the curvature scale of the SMEFT field space [24]. In this way, recent studies in the SMEFT context have clarified implications of perturbative unitarity for scalar field theories in particular.…”

Unitarity violation and the geometry of Higgs EFTs

“…However, the connection between unitarity and geometry has remained obscure. It has long been known that scattering amplitudes probe the local geometry of the scalar manifold [7,[17][18][19]; for example, the leading-in-energy terms in 2-to-2 scattering amplitudes…”